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Mathematics
Fractals
1. Introduction to Fractals
2. Mathematical Foundations
3. Fractal Dimension
4. Classical Fractals
5. Iterated Function Systems
6. Escape-Time Fractals
7. Random and Stochastic Fractals
8. Fractals in Nature
9. Applications of Fractal Geometry
10. Connections to Related Fields
11. Computational Methods and Tools
12. Advanced Topics and Current Research
Classical Fractals
Linear Fractals
Cantor Set
Construction Process
Properties and Characteristics
Variations and Generalizations
Koch Curve
Construction Algorithm
Koch Snowflake
Dimension Calculation
Sierpiński Triangle
Iterative Construction
Chaos Game Method
Pascal's Triangle Connection
Sierpiński Carpet
Construction Process
Three-Dimensional Extension
Space-Filling Curves
Peano Curve
Hilbert Curve
Dragon Curve
Lévy C Curve
Three-Dimensional Fractals
Menger Sponge
Construction Process
Properties and Dimension
Tetrix (Sierpiński Tetrahedron)
Jerusalem Cube
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3. Fractal Dimension
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5. Iterated Function Systems